The boy, a 6-year-old kindergartner at Mather Elementary School in Dorchester, had never ridden a school bus before. But when Smith’s work schedule changed, she reluctantly signed her child up for transportation.

Samuel “Sammy’’ Aaron rode the bus just once and his mother has regretted it ever since. That Wednesday afternoon in early January, Jennifer Smith arrived at the Mattapan bus stop on time, but her son failed to show. As the minutes passed, her worry turned to panic.

Finally, 16 minutes after his bus was due, her cellphone rang: It was a stranger, saying she had found the boy crying near Franklin Park, more than a mile away. Luckily, Sammy knew his mother’s cellphone number.

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The incident, confirmed by a School Department spokesman, occurred Jan. 4, on students’ first day back at school after Christmas vacation, and followed months of frustration over tardy bus arrivals at Boston public schools. In December, the school system fined its transportation provider $800,000 for late bus arrivals last fall. The bus company, First Student Inc., is under contract to deliver more than 30,000 students to and from school on 600 buses.

Smith says it wasn’t until she voiced her frustration at a parent council meeting nearly a week later, on Jan. 10, that she received a call back. A parent who attended the meeting e-mailed a Globe reporter about the incident and made school officials aware that she had done so.

A day or two later, Smith says, she received a voicemail from Michael Hughes, transportation director for the Boston public schools, saying that her son’s bus driver would be disciplined, and promising to call her back. That call never came, Smith says, though she left two more messages.

On Thursday - a month after her son was left to wander city streets alone, and days after a reporter began asking school officials about the incident - Smith finally received another call from Hughes, and heard, for the first time, an apology and an explanation of what happened.

A spokesman for the school system, Matthew Wilder, called the driver’s error and the delayed response from officials “an unacceptable situation.’’

“The boy should never have been left at the wrong stop, and the response on our end should have been better,’’ he said. “Any incident like this is troubling to us.’’

Smith was thankful that Sammy was safe but deeply bothered by officials’ seeming unconcern. “It could have turned out so much worse,’’ she said.

The 6-year-old’s trip home that day began well. At Mather Elementary, Wilder said, the vice principal went “beyond standard procedure’’ to ensure that his first bus ride would go smoothly, introducing him to the driver and telling her exactly where his stop would be.

The bus left the school about 3:30 p.m. When it reached the corner of Blue Hill Avenue and Johnston Road, a stop where seven pupils usually get off, Sammy Aaron got off, too. At the time, the driver was distracted by an incident on the bus and a pupil who was upset, Wilder said, though he stressed that the distraction was not an excuse.

A mile away, at Blue Hill Avenue and Almont Street, Smith was waiting at the assigned corner well before 4:04 p.m., when the bus was scheduled to arrive, she said. At 4:05 p.m., she called the school and was assured her son had boarded the right bus. Finally, close to 4:20 p.m., her cellphone rang. It was an unfamiliar number, but when she answered, she could hear her only child crying in the background.

A stranger said she had found the boy wandering near Franklin Park. The two women arranged to meet at a fire station. When Smith got there, shortly after 4:30 p.m., Sammy was still crying, she said.

“He was in the car and he was warm, but he was shaking,’’ she said. “I had never seen Sammy like that before.’’

The boy was found more than a half-mile from where he got off the bus. In an interview, he described what happened: “I got out of the bus, and there were two girls with me, and they said home was down there,’’ he said. “They left me by myself, and I was running, but my legs got tired.’’

When Smith first called the transportation office late that afternoon to complain, the manager on duty should have been alerted immediately, Wilder said. Instead, the complaint was forwarded to First Student, the bus company, causing delay.

The next day, Jan. 5, Smith and her son’s vice principal called the transportation office together from the school. Smith says she was transferred from one employee to another and repeated her story several times, but no one could answer her questions.

Hughes, the transportation director, did not learn about the incident until four days later, on Jan. 9, when the Mather vice principal called him again, Wilder said. After an investigation and a suspension of one or two days, the driver received a warning, was reassigned to a different route, and attended a two-hour retraining session to review bus procedures.